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Reconstruction and application of reforming textbook problems for mathematical modeling process (수학적 모델링 과정을 반영한 교과서 문제 재구성 예시 및 적용)

  • Park, SunYoung;Han, SunYoung
    • The Mathematical Education
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    • v.57 no.3
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    • pp.289-309
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    • 2018
  • There has been a gradually increasing focus on adopting mathematical modeling techniques into school curricula and classrooms as a method to promote students' mathematical problem solving abilities. However, this approach is not commonly realized in today's classrooms due to the difficulty in developing appropriate mathematical modeling problems. This research focuses on developing reformulation strategies for those problems with regard to mathematical modeling. As the result of analyzing existing textbooks across three grade levels, the majority of problems related to the real-world focused on the Operating and Interpreting stage of the mathematical modeling process, while no real-world problem dealt with the Identifying variables stage. These results imply that the textbook problems cannot provide students with any chance to decide which variables are relevant and most important to know in the problem situation. Following from these results, reformulation strategies and reformulated problem examples were developed that would include the Identifying variables stage. These reformulated problem examples were then applied to a 7th grade classroom as a case study. From this case study, it is shown that: (1) the reformulated problems that included authentic events and questions would encourage students to better engage in understanding the situation and solving the problem, (2) the reformulated problems that included the Identifying variables stage would better foster the students' understanding of the situation and their ability to solve the problem, and (3) the reformulated problems that included the mathematical modeling process could be applied to lessons where new mathematical concepts are introduced, and the cooperative learning environment is required. This research can contribute to school classroom's incorporation of the mathematical modeling process with specific reformulating strategies and examples.

A rapid modeling method and accuracy criteria for common-cause failures in Risk Monitor PSA model

  • Zhang, Bing;Chen, Shanqi;Lin, Zhixian;Wang, Shaoxuan;Wang, Zhen;Ge, Daochuan;Guo, Dingqing;Lin, Jian;Wang, Fang;Wang, Jin
    • Nuclear Engineering and Technology
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    • v.53 no.1
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    • pp.103-110
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    • 2021
  • In the development of a Risk Monitor probabilistic safety assessment (PSA) model from the basic PSA model of a nuclear power plant, the modeling of common-cause failure (CCF) is very important. At present, some approximate modeling methods are widely used, but there lacks criterion of modeling accuracy and error analysis. In this paper, aiming at ensuring the accuracy of risk assessment and minimizing the Risk Monitor PSA models size, we present three basic issues of CCF model resulted from the changes of a nuclear power plant configuration, put forward corresponding modeling methods, and derive accuracy criteria of CCF modeling based on minimum cut sets and risk indicators according to the requirements of risk monitoring. Finally, a nuclear power plant Risk Monitor PSA model is taken as an example to demonstrate the effectiveness of the proposed modeling method and accuracy criteria, and the application scope of the idea of this paper is also discussed.

A Constructive Modeling Process in the Form of 'Visual Mathematics' (시각수학과 원리 확장적 모델링 프로세스)

  • 김진희
    • Archives of design research
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    • v.12 no.2
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    • pp.89-95
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    • 1999
  • Carlo H. Sequin, a computer scientist, became to know a sculpture of subtle space construction which was created by Brent Collins, a sculptor, and introduced it as 'Visual Mathematics' in a journal. Sequin who was able to deduce a basic logic of the construction, has developed a software which can be used for virtual modeling merely by substituting simple numerical values using a computer and supplied it to Collins. The present author who was exposed to their collaboration works through series of their papers published in the journal, Leonardo, introduces the Collins' sculptures and the author's modeling procedures of animation works both of which show many common things in visual characteristics and modeling expansion method. The author investigates the mathematical characteristics which is used as a basic motive of modeling and then supplied as a principal visual characteristics of a material. 'Modeling Development by Principle Expansion,' in which the expansion is developed on the base of space twist as for Collins whereas the space section as for the present author, is introduced in this study. With the same stream of the mutual reaction in 'arts, sciences and technology' which has been stressed with the development of sciences and technology, this modeling technology is suggested as a research theme which has a possiblity of various applications.

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An User Interface hierarchical modeling process based on Metamodel (메타모델 기반 사용자 인터페이스 계층적 모델링 프로세스)

  • Song, Chee-Yang;Cho, Eun-Sook;Kim, Chul-Jin
    • Journal of Korea Multimedia Society
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    • v.11 no.4
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    • pp.525-543
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    • 2008
  • Recently, the scope of user interface is increasing the relative importance in software development dramatically. As a result, there are various relative technologies like as SWING, MFC, Web 2.0, and etc. However, most current software developments are progressed in separate development process with user interface part and business part respectively. This causes the problems, like as a difficulty in the integration process, an development period's delay, and a poor reusability for the constructed models. That is, the extendability and reusability of the created models is being decreased because UI modeling is not systematic and hierarchical, and the consistent integration technique between UI modeling and business modeling does not supported. To solve these problems, this paper proposes an unified and systematic UI modeling process based on UML, using the hierarchical metamodel according to the abstraction levels of development phase. We suggest an UI metamodel, which contains a hierarchy by layering the modeling elements in PIM and PSM based on maturity degree of the development. An hierarchical modeling process combined UI modeling and business modeling is built by applying the UI and business metamodel in terms of three modeling phases(concept/specification/concrete). The effectiveness of the modeling process is shown by applying the proposed process into an Internet Shopping Mall System. Through the exploratory results, the hierarchical UI metamodel and process can produce systematic and layered UI models. This can improve the quality and reusability of models.

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ViP: A Practical Approach to Platform-based System Modeling Methodology

  • Um, Jun-Hyung;Hong, Sung-Pack;Kim, Young-Taek;Chung, Eui-Young;Choi, Kyu-Myung;Kong, Jeong-Taek;Eo, Soo-Kwan
    • JSTS:Journal of Semiconductor Technology and Science
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    • v.5 no.2
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    • pp.89-101
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    • 2005
  • Research on highly abstracted system modeling and simulation has received a great deal of attention as of the concept of platform based design is becoming ubiquitous. From a practical design point of view, such modeling and simulation must consider the following: (i) fast simulation speed and cycle accuracy, (ii) early availability for early stage software development, (iii) inter-operability with external tools for software development, and (iv) reusability of the models. Unfortunately, however, all of the previous works only partially addresses the requirements, due to the inherent conflicts among the requirements. The objective of this study is to develop a new system design methodology to effectively address the requirements mentioned above. We propose a new transaction-level system modeling methodology, called ViP (Virtual Platform). We propose a two-step approach in the ViP method. In phase 1, we create a ViP for early stage software development (before RTL freeze). The ViP created in this step provides high speed simulation, lower cycle accuracy with only minor modeling effort.(satisfying (ii)). In phase 2, we refine the ViP to increase the cycle accuracy for system performance analysis and software optimization (satisfying (i)). We also propose a systematic ViP modeling flow and unified interface scheme based on utilities developed for maximizing reusability and productivity (satisfying (ii) and (iv)) and finally, we demonstrate VChannel, a generic scheme to provide a connection between the ViP and the host-resident application software (satisfying (iii)). ViP had been applied to several System-on-a-chip (SoC) designs including mobile applications, enabling engineers to improve performance while reducing the software development time by 30% compared to traditional methods.

Efficient parameters to predict the nonlinear behavior of FRP retrofitted RC columns

  • Mahdavi, Navideh;Ahmadi, Hamid Reza;Bayat, Mahmoud
    • Structural Engineering and Mechanics
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    • v.70 no.6
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    • pp.703-710
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    • 2019
  • While fiber-reinforced plastic (FRP) materials have been largely used in the retrofitting of concrete buildings, its application has been limited because of some problems such as de-bonding of FRP layers from the concrete surface. This paper is the part of a wide experimental and analytical investigation about flexural retrofitting of reinforced concrete (RC) columns using FRP and mechanical fasteners (MF). A new generation of MF is proposed, which is applicable for retrofitting of RC columns. Furthermore, generally, to evaluate a retrofitted structure the nonlinear static and dynamic analyses are the most accurate methods to estimate the performance of a structure. In the nonlinear analysis of a structure, accurate modeling of structural elements is necessary for estimation the reasonable results. So for nonlinear analysis of a structure, modeling parameters for beams, columns, and beam-column joints are essential. According to the concentrated hinge method, which is one of the most popular nonlinear modeling methods, structural members shall be modeled using concentrated or distributed plastic hinge models using modeling parameters. The nonlinear models of members should be capable of representing the inelastic response of the component. On the other hand, in performance based design to make a decision about a structure or design a new one, numerical acceptance should be determined. Modeling parameters and numerical acceptance criteria are different for buildings of different types and for different performance levels. In this paper, a new method was proposed for FRP retrofitted columns to avoid FRP debonding. For this purpose, mechanical fasteners were used to achieve the composite behavior of FRP and concrete columns. The experimental results showed that the use of the new method proposed in this paper increased the flexural strength and lateral load capacity of the columns significantly, and a good composition of FRP and RC column was achieved. Moreover, the modeling parameters and acceptance criteria were presented, which were derived from the experimental study in order to use in nonlinear analysis and performance-based design approach.

A Study on the Direction of Modeling Techniques for the Development of Large Scale Software (큰 규모 소프트웨어의 개발을 위한 모델링 기법의 방향성에 대한 연구)

  • Cho, Min-Ho
    • The Journal of the Korea institute of electronic communication sciences
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    • v.15 no.1
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    • pp.167-172
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    • 2020
  • The importance of modeling in large-scale software development has already been confirmed. In most of the projects, modeling is done using UML. However, UML is a class-based modeling tool, which is complicated and lacks in modeling common modules, components, processes, and data. To supplement this point, this paper will help the actual industrial field by suggesting the integration of various modeling techniques, including structural methodology and information engineering methodology developed in the computer field. Through this paper, I would like to show that it is useful to use various methodologies instead of using UML to develop software that satisfies customers.

A Study on Meta-Level Learning through Modeling Activities (모델링 활동을 통한 메타수준 학습에 대한 연구)

  • Park, JinHyeong;Lee, Kyeong-Hwa
    • School Mathematics
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    • v.16 no.3
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    • pp.409-444
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    • 2014
  • There have been many discussions of teaching and learning mathematics through modeling activities in mathematics education research community. Although there has been some agreement regarding modeling activity as an alternative way to support mathematics teaching and learning, there is still no clear consensus on these issues. This paper reports a case study which aims to identify ways to design modeling tasks and instruction to foster meta-level learning, and investigate how modeling activities can facilitate meta-level learning. From the results of teaching experiment, this study examines the potential of modeling activities in mathematics teaching and learning.

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Application of UML (Unified Modeling Language) in Object-oriented Analysis of Microarray Information System (UML을 활용한 마이크로어레이 정보시스템의 객체지향분석)

  • Park, Ji-Yeon;Chung, Hee-Joon;Kim, Ju-Han
    • Proceedings of the Korean Society for Bioinformatics Conference
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    • 2003.10a
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    • pp.147-154
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    • 2003
  • Microarray information system is a complex system to manage, analyze and interpretate microarray gene expression data. Establishment of well-defined development process is very essential for understanding the complexity and organization of the system. We performed object-oriented analysis using Unified Modeling Language (UML) in specifying, visualizing and documenting microarray information system. The object-oriented analysis consists of three major steps: (i) use case modeling to describe various functionalities from the user's perspective (ii) dynamic modeling to illustrate behavioral aspects of the system (iii) object modeling to represent structural aspects of the system. As a result of our modeling activities we provide the UML diagrams showing various views of the microarray information system. We believe that the object-oriented analysis ensures effective documentations and communication of information system requirements. Another useful feature of object-oriented technique is structural continuity to standard microarray data model MAGE-OM (Microarray Gene Expression Object Model). The proposed modeling e(forts can be applicable for integration of biomedical information system.

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Stakeholders Driven Requirements Engineering Approach for Data Warehouse Development

  • Kumar, Manoj;Gosain, Anjana;Singh, Yogesh
    • Journal of Information Processing Systems
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    • v.6 no.3
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    • pp.385-402
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    • 2010
  • Most of the data warehouse (DW) requirements engineering approaches have not distinguished the early requirements engineering phase from the late requirements engineering phase. There are very few approaches seen in the literature that explicitly model the early & late requirements for a DW. In this paper, we propose an AGDI (Agent-Goal-Decision-Information) model to support the early and late requirements for the development of DWs. Here, the notion of agent refers to the stakeholders of the organization and the dependency among agents refers to the dependencies among stakeholders for fulfilling their organizational goals. The proposed AGDI model also supports three interrelated modeling activities namely, organization modeling, decision modeling and information modeling. Here, early requirements are modeled by performing organization modeling and decision modeling activities, whereas late requirements are modeled by performing information modeling activities. The proposed approach has been illustrated to capture the early and late requirements for the development of a university data warehouse exemplifying our model's ability of supporting its decisional goals by providing decisional information.